Continuous-flow microfluidic biochips are a type of biochip technology based on microfluidic channels that enable various biological experiments and analyses to be performed on a tiny chip. They have the advantages of a high throughput, high sensitivity, high precision, low cost, and quick response. In the architectural synthesis of continuous-flow microfluidic biochips (CFMBs), prior work has not considered reducing component interconnection requirements, which led to an increase in the number of connection pairs. In this paper, we propose an architectural synthesis flow for continuous-flow microfluidic biochips with connection pair optimization, which includes high-level synthesis, placement, and routing. In the high-level synthesis stage, our method reduces the need for component interconnections, which reduces the number of connection pairs. Our method performs fine-grained binding, ultimately obtaining high-quality binding and scheduling results for flow paths. Based on the high-quality binding results, we propose a port placement strategy based on port correlation and subsequently use a quadratic placer to place the components. During the routing stage, we employ a conflict-aware routing algorithm to generate flow channels to reduce conflicts between liquid transportation tasks. Experimental results on multiple benchmarks demonstrate the effectiveness of our method. Compared with the existing work, the proposed algorithm obtains average reductions of 35.34% in connection pairs, 24.30% in flow channel intersections, 21.71% in total flow channel length, and 18.39% in the execution time of bioassays.